For an ELP \(\Pi = (\mathcal {A}, \mathcal {E}, \mathcal {R})\) , the epistemic reduct
[1]} of the program \(\Pi \)  w.r.t. a guess \(\Phi \) , denoted \(\Pi ^\Phi \) ,
consists of the rules \(\mathcal {R}^\Phi =\lbrace  r^\lnot \mid r \in \mathcal {R}\rbrace \) , where \(r^\lnot \)  is defined
as the rule \(r \in \mathcal {R}\)  where all occurrences of epistemic literals \(\mathbf {not}\,\ell \in \Phi \)  are replaced by \(\top \) , and all remaining epistemic negation
symbols \(\mathbf {not}\,\)  are replaced by default negation \(\lnot \) . Note that, after this
transformation, \(\Pi ^\Phi =(\mathcal {A},\mathcal {R}^\Phi )\)  is a logic program without epistemic
negationIn fact, \(\Pi ^\Phi \)  may contain triple-negated atoms
\(\lnot \lnot \lnot a\) . But, according to the definition of the GL-reduct in
[2]}, such formulas are equivalent to simple negated atoms
\(\lnot a\) , and we treat them as such.. This leads to the following, central
definition.
